From the solved models, the velocities and the drag forces (the magnitudes of the force components of the cruising direction exerted on the bus) (FX) were assessed at 20 km∙h−1 for three different geometries and induced flows.
3.1. Velocity Plots
To represent the typical flow patterns around the bus, velocity magnitudes were collected. The origin point of the coordinate system was the front plate of the bus, which was located on the ground and in the centre of the domain (see
Figure 3). The velocity distribution on the X-Y plane was shown by the longitudinal midplane view.
Figure 5 depicts the rear wake zones for the three bus types. The plane began after the rear plane of the bus at 12.5 m and ended 12 m further way, when the flow could be regarded as undisturbed. Velocities were normalized to the cruising speed of 20 km∙h
−1. The peak velocity was 1.89, which developed at the frontal corners of the bus; this number was chosen as the maximum value of the scale. Figures for the visual comparison were taken at the sixty-second mark of the simulation flowtime.
The rear wake region length was roughly 2 m long in all the three models, yet additional shedding could also be observed. Since the shedding occurred stochastically, the velocity plots were not synchronized; thus, the comparison of the sizes of the wake structure could not be made. However, it can be noted that the upper recirculation bubble was larger in all three cases. The same was observed in some experimental measurements in the work of Lajos et al. [
18], which was attributed to the moving ground. The most notable change that could be noticed is in
Figure 5b; the recirculation bubble was roughly 0.25 m higher, due to the rear position of the AC, yet, in length it showed only a half-meter increase.
The AC had to be evaluated also, for additional comparison. When the AC was in the front, the wake region was shorter than when it was at the back (see
Figure 6). The wake region behind the AC was steeper in the rear position, as shown in
Figure 6b, because it was located at the tail end of the vehicle. In
Figure 6a, a small stagnation point can be also seen on the leading edge, indicating that the frontal position could cause an upward induced drag. While there was no sign of stagnation in model B, the frontal circulation bubble of the AC was approximately half a metre larger. As numerous studies show [
7], covering these wake regions may result in less drag loss. The reason for this disadvantageous shape could be flexibility and the small size of the AC. According to
Figure 6, different shapes should be defined, depending on whether the AC is in the front or at the rear.
The wake region was also evaluated at three different Y-Z planes, at X = 12.5 m, 13 m, and 14 m, for the three models. The results of models A, B and C (
Figure 7) were similar to the plots in Ref. [
12].
Figure 7a–c show the formation of longitudinal wakes. In
Figure 7d–f, further development can be seen immediately after half a meter. After an additional 1 m, the rear wake region detached into four regions, as measured by particle image velocimetry (PIV) in the work of Gurlek et al. [
19].
Figure 7c shows a slight distortion, with two bright lines at Y = 0.6 m and 1.2 m, which were attributed to the absence of prismatic layers at the AC outlets. However, this distortion only affected a small portion of the assessed area, and the effect become insignificant in
Figure 7f.
To examine the symmetricity of the flow, horizontal (Z-X) planes were added at the height of the axis of the fan in model C (Y = 0.91 m). In all three models, it can be seen in
Figure 8a,c,e that the flow slightly deformed towards the negative Z range (left-hand side of the bus). This asymmetric pattern could also be seen when the time-averaged drag force was assessed (see
Figure 8b,d,f). It showed that the drag force on the left-hand side was noticeably larger than on the right-hand side. The difference between the mean values of both sides was greater than the standard deviation, indicating that the difference was noteworthy. It could be contributed to the following phenomena: by default, due to vortex shedding, a symmetric flow-pattern could not develop; an asymmetric pattern always develops with a bias to one side; due to the size differences of the mirrors, the flow was distorted. Because low velocity can produce unsteady flow patterns, visual assessment alone could not detect this bias. It would be preferable to use more time-samples or additional time-averaged values. Further time-samples were not shown, since the sheddings on
Figure 8 were not synchronized.
3.2. Induced Flow Patterns
When the AC was turned on, all the three wake structures changed.
Figure 9 depicts the disturbed wake regions for all three models. Because these were the most significant changes, minor changes in the flow structure were not examined. Comparing
Figure 6a,b with
Figure 9a,b, it could be seen that when it was placed on the top, a wake region formed. The height of this wake region was approximately 0.75 m, and it increased close to the trailing edge. The model A stagnation point was not visible, indicating that the induced flow near to the leading edge was able to reduce its magnitude.
Figure 9a also shows that the frontal circulation bubble was reduced in size by half. When the AC was turned on, model B had a slightly longer circulation bubble compared to when it was off. In length, the wake region had similar dimensions. At approximately 1 m, the velocity started to build up again. This effect could indicate that the induced flow generated an induced drag; thus, aerodynamic losses could be expected in the case of model A and B, while in model C (see
Figure 9c), when the fans were turned on, it disturbed the lower rear wake region. This disturbance reduced the lower recirculation bubble, and so a drag-loss reduction could be expected.
3.3. Q-Criterion
The Q-criterion [
20] was used to depict the vortices, where
Q was the second invariant of the velocity gradient tensor,
S and
Ω were the symmetric and antisymmetric parts of the tensor, respectively, and
Q was expressed with Equation (1).
Model B was suitable to present the Q-criterion value formations at 90 s
−2 in
Figure 10. The cluster of hairpin vortices could be seen on the leading edges of the bus, which correspond to the results of Ref. [
21]. The O-shaped vortices appeared as a result of the position of the AC inlets and outlets and of the flow. The growth trend was previously seen in
Figure 9a,b, but the actual form can only be seen in
Figure 10. During the literature search, no examples of these types of O-rings were discovered. They were only found when the O-ring formed on the rear surface [
21]. This vortex dissipated as soon as it detached from the AC. Lastly, from
Figure 10, large number of vortices can be seen forming around the side-view mirrors. Usually, vortices around mirrors are not evaluated directly, but a more relevant factor is the noise load caused by the increased velocities [
22,
23,
24].
3.4. Force Values
The drag forces (F
X) were previously mentioned in
Section 3.1, where the uneven distribution on the sides was noted. The F
X was the sum of the forces, yet the magnitude was low. The reason for this was that each individually investigated surface (e.g., left-hand and right-hand side) included peaking areas such as the trailing edges on the front, which reduced the F
X magnitudes on the sides or the roof. The same occurred on the front, where the F
X, caused by the stagnation pressure, was reduced by the same trailing edge.
Figure 11a depicts the frontal and rear surface F
X deviations. Because of the constant load from the wind-tunnel flow, the deviation on the frontal surface was smaller. The fluctuations could be caused by the right-hand side-view mirror, which was located on the front of the bus, and they could also be amplified by the corner vortices. On the rear end, the fluctuation was more noticeable. As previously stated in
Section 3.1, shedding occurred. However, because it lacked a distinct pattern, comparing it with a wave function would have yielded low regression values.
The sum of F
X was obtained from the three models and at three different AC flow rates. Because at 20 km∙h
−1 relevant changes occurred rather than a time-averaged value, the mean and standard deviation should always be mentioned. When the AC was turned on, the baseline scenario (
Figure 11b) showed a slight increase. This change could not be noticed, because of the deviation. The deviation at model B (see
Figure 11c) become smaller, and the change was not noticeable when the AC was less than 50% of its maximum flow-rate. When it reached the maximum flow-rate, there was a noticeable increase. When the AC flow was induced, only model C had a decreased F
X (see
Figure 11d). It was also worth noting that model C had the lowest F
X. The main reason for this could be that the AC was missing, and thus the wakes caused by it were absent.
3.5. Drag Coefficients
The best way to quantify aerodynamic losses was the application of drag coefficient (
CD), which was calculated using the following equation:
where
FX was the sum of the force components,
A was the projection area,
vc was the velocity of the bus in the cruising direction (20 km∙h
−1), and
ρ was the density of air (1.225 kg/m
3). Since the projected area could change when the AC was removed, the corresponding projected areas were used. When the projected area was kept at baseline, a pseudo change in drag loss occurred.
The
CD values showed that the AC flow rate had only a minor effect on the aerodynamic loss. It could also be concluded that removing the AC box (model C) resulted in a
CD reduction of at least 8%, and even more if the flow rate increased. This was the most significant change, because it was greater than the standard deviation. It was worth noting that the one-count drag reduction in model B is doubtful, because the
CD deviation was more than ten times greater than the improvement. According to the results in
Table 4, the aerodynamic optimum at 20 km∙h
−1 was in the model C design at the 3480 m
3∙h
−1 flow rate, which resulted in a 12%
CD reduction compared with the baseline scenario.
3.6. Validation
When one uses a 1:1 model, an experimental aerodynamic assessment of buses is difficult. In other cases, if the velocity is achievable, small-scale models can be used. Furthermore, at low speeds on a blunt body, shedding occurs, increasing the uncertainty of the measurement. As a result, because this paper only focuses on proposing an alternative position for the AC, only numerical models were used. Validation is divided into two parts: a flow pattern and a CD comparison.
With the pure visual assessment [
18,
19] which had been made previously, the flow pattern described was similar to the result of this numerical study, including the shape of the rear wake region, the lower horseshoe vortices, and the clusters of hairpin vortices [
21].
Because drag coefficients for buses are rarely investigated, only a few publications can serve as comparable data.
Table 5 strengthens the fact that, as the speed of the vehicle decreases, so does the
CD [
25]. At high speeds, in the case of buses, the
CD is usually relatively large, and these values are more acceptable for blunt bodies. However, in urban areas, where the average speed is lower [
17], another
CD should be used. Furthermore, the use of a side-view mirror does not significantly change the
CD; the change is in the range of the standard deviation.
Based on independent numerical and experimental measurement, the current numerical results were in good agreement. However, limitations must be mentioned. Because the applied model was isothermal, it was assumed that the flow temperature from the AC had no significant effect on the flow rate, and did not generate flow structures. Because the numerical models were solved at a low speed, value fluctuations and unsteadiness affected the standard deviations of the examined indicators.